Degradation of an optical pulse propagating through an optical fiber is the result of attenuation and dispersion. Dispersion is the broadening of discrete data bits as they propagate through the media. Pulse broadening results in an overlap between sequential data bits causing an increase in the uncertainty whether a bit is interpreted as logic 0 or 1. This uncertainty in logic state is quantified in terms of bit error rate (BER), where the BER is defined as the number of error bits divided by the total number of bits transmitted in a given period of time. For high-speed Ethernet, the BER cannot exceed 1 error bit for every 1 trillion bits transmitted (BER<10−12). There are two contributions to the total dispersion in multimode fiber: chromatic dispersion, or material dispersion, and modal dispersion.
Chromatic or material dispersion occurs because the refractive index of a material changes with the wavelength of light. This is due to the characteristic resonance frequencies at which the material responds to light (light is a propagating electromagnetic field). Shorter wavelengths encounter a higher refractive index (i.e., greater optical density) and consequently travel slower than longer wavelengths. Since a pulse of light typical comprises several wavelengths, the spectral components of the optical signal spread in time, or disperse, as they propagate, causing the pulse width to broaden.
Optical fiber is nearly pure silica (SiO2), so the chromatic or material dispersion of fiber is essentially the same as pure fused silica. In FIG. 1 we plot the material dispersion of fused silica and the refractive index as a function of wavelength. Since the refractive index of a material is wavelength dependent, n(λ), the velocity of light in a material is also wavelength dependent related by,
                              v          ⁡                      (            λ            )                          =                  c                      n            ⁡                          (              λ              )                                                          (        1        )            Where, c is the speed of light in vacuum (299,792,458 meters/second).
Referring to Equation 1, the refractive index for a short wavelength (referred to as “blue” light) is larger than that for a longer wavelength (referred to as “red” light) so that light of longer wavelengths (“red”) travels faster than shorter wavelengths (“blue”).
For light traveling through a medium with this characteristic, the effect is called “normal” dispersion. If the refractive index for shorter wavelengths is lower than longer wavelengths, the dispersion is called anomalous, as blue light will travel faster than red light.
In addition to material dispersion, optical signals traversing optical waveguides such as a multimode fiber optic cable (MMF) also undergo modal dispersion, which is generally a much larger effect in MMF. Due to the wave nature of light and the wave-guiding properties of optical fiber, an optical signal traverses the fiber along discrete optical paths called modes. The optical power of the pulse is carried by the sum of the discrete modes. With reference to FIGS. 2A and 2B, MMF is optimized so that all modes arrive at the output of the fiber at the same time. This is achieved by adjusting or “grading” the refractive index profile of the fiber core. Modes traveling with larger angles (and consequently traverse longer distances) must travel faster. These are called high-order modes. Modes traveling with small angles (low-order modes) travel slower in graded-index fiber. The difference in propagation delays between the fastest and slowest modes in the fiber is used to determine the inter-modal dispersion or simply modal dispersion.
To minimize modal dispersion, standard Graded Index Multimode Fiber (GI-MMF) is designed so the index of refraction across the core follows a parabolic distribution (referred to herein as the standard parabolic refractive index profile). The formula describing the radial distribution in refractive index for minimum modal dispersion is given by
                              n          ⁡                      (            r            )                          =                                            n              1                        ⁡                          [                              1                -                                  2                  ⁢                                                            (                                              r                        R                                            )                                        α                                    ⁢                  Δ                                            ]                                            1            2                                              (        2        )            Where α is a number close to 2 (and specific to each fiber manufacturer), R is the radius of the fiber core and Δ is given by
                    Δ        =                                            n              1              2                        -                          n              2              2                                            2            ⁢                                                  ⁢                          n              1              2                                                          (        3        )            
The metric used to characterize modal dispersion in MMF is Differential Mode Delay (DMD), specified in Telecommunications Industry Association Document No. TIA-455-220-A and expressed in units of picoseconds per meter (ps/m) so that the total delay is normalized by fiber length. Low modal dispersion as measured by DMD generally results in higher-bandwidth MMF. Better control in the manufacturing process produces a profile closer to the standard parabolic refractive index profile which minimizes modal dispersion. It would be desirable to make changes to the standard parabolic refractive index profile to compensate for the wavelength distribution and emission pattern of a light source to reduce modal dispersion beyond current capabilities. Furthermore, it would be desirable that these changes be included in current MMF test methods to accurately characterize DMD and fiber bandwidth.